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<math>\sigma</math>  = odd
 
<math>\sigma</math>  = odd
  

Revision as of 15:25, 9 September 2008

Question: Show that if H is a subgroup of $ S_n $, then either every member of H is an even permutation or exactly half of the members are even.

Answer: Suppose H contains at least one odd permutation, say $ \sigma $. For each odd permutation $ \beta $, the permutation $ \sigma \beta $ is even.

Note:

$ \sigma $ = odd

$ \beta $ = odd

$ \sigma \beta $ = even

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